1. Put each in your calculator and check what y equals when x = 90.

2. Chapter 2: Functions and Models Lesson 6: Quadratic Models Mrs. Parziale

3. Vocabulary Quadratic models: models based on quadratic functions

4. Properties of Quadratics: Parabola opens upward for a>0 (positive) and downward for a<0 (negative). Vertex is the place where the axis of symmetry and the parabola intersect. Vertex is the minimum for a>0 and maximum for a<0

5. Domain: all real numbers Range: depends on the location of the vertex. (range ≥ min or range ≤ max) The x-intercepts are the solution to f(x) = 0 (done either by factoring or the quadratic formula). The y-intercept is (0, c).

6. Example 1: Consider f(x) = 2x 2 – 9x + 3 (a) Find its x- and y-intercepts (b) Tell whether the parabola has a maximum or minimum point, and find the coordinates of the vertex.

8. Example 2: Physics application – Famous quadratic model = Newton’s Formula for Height of an Object Thrown Vertically where g = accel. due to gravity (9.8 for m/s 2 and 32 for ft/s 2 ). A projectile shot from a tower 10 feet high with an upward velocity of 100 feet/second. (a) Approximate the relationship between height (h) in feet and time (t) in seconds after the projectile is shot. (formula) (b) How long will the projectile be in the air?

10. Example 3: A pizza is sliced by a number of straight cuts as shown below. The table shows the greatest number of pieces f(n) into which it can be sliced by n cuts. a. Fit a quadratic model to these data. b. Use your model to find the greatest number of pizza pieces produced by 5 straight cuts. n01234 f(n)124711

11. Closure Given the following quadratic function: What is the y-intercept? Does this parabola have a min or max? How do you find the zeros (x-intercepts)? What is the domain? Range?